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Ivahew [28]
3 years ago
5

Classify triangle ABC by its sides if side AB = 6x, side AC = 4x + 6 and side BC = 8x + 3. The perimeter of triangle ABC is 63.

Show all your work.
Mathematics
1 answer:
wolverine [178]3 years ago
4 0

Answer:

So the triangle ABC is an isosceles triangle

Step-by-step explanation:

By definition the perimeter of a triangle is equal to the sum of the lengths of its sides.

In this case we know that the perimeter is 63

The lengths of its sides depend on x.

AB = 6x\\AC = 4x + 6\\BC = 8x + 3

So:

6x + 4x + 6 + 8x + 3 = 63

Now we solve for the variable x.

6x + 4x + 6 + 8x + 3 = 63

18x + 9 = 63

18x = 54

x=\frac{54}{18}\\\\x=3

Therefore:

AB = 6(3)=18\\AC = 4(3)+6=18\\BC = 8(3) + 3=27

The triangle has two sides of equal length. The triangles that have two equal sides are the isosceles triangles.

So the triangle ABC is an isosceles triangle

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Sandy drives in town at a rate of 25 miles per hour. It takes her 15 minutes to drive to the store. How far is it to the store?
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Answer: 6.25 miles

Step-by-step explanation:

Convert the 15 minutes to 1/4 hr or .25

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6 0
3 years ago
Find all pairs of natural numbers which can be the solution to the equation a+b=42.
Setler [38]

Answer:

(1,41), (2,40), (3,39), (4,38), (5,37), (6,36), (7,35), (8,34), (9,33), (10,32), (11,31), (12,30), (13,29), (14,28), (15,27), (16,26), (17,25), (18,24), (19,23), (20,22), (21,21), (22,20), (23,19), (24,18), (25,17), (26,16), (27,15), (28,14), (29,13), (30,12), (31,11), (32,10), (33,9), (34,8), (35,7), (36,6), (37,5), (38,4), (39,3), (40,2), (41,1).

Step-by-step explanation:

To find all pairs of natural numbers which are solution to a+b=42, we need to first choose a value to one of them (let's choose 'a'), and that value will be the lowest possible, so we begin with a=1, and then we increase to 2, and 3, and so on.

For each value of a, we calculate the value of b using the equation.

So, starting with a=1, we have that b=41

Then, with a=2, we have that b=40, and so on.

Doing this until a=41 (so b=1 will be the lowest value possible for b), we have the pairs of natural number we want:

(1,41), (2,40), (3,39), (4,38), (5,37), (6,36), (7,35), (8,34), (9,33), (10,32), (11,31), (12,30), (13,29), (14,28), (15,27), (16,26), (17,25), (18,24), (19,23), (20,22), (21,21), (22,20), (23,19), (24,18), (25,17), (26,16), (27,15), (28,14), (29,13), (30,12), (31,11), (32,10), (33,9), (34,8), (35,7), (36,6), (37,5), (38,4), (39,3), (40,2), (41,1).

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3 years ago
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AysviL [449]

Answer:

(11x+7)(3x−2)

3 0
3 years ago
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